Idempotent mathematics is a rapidly developing new branch of the mathematical sciences that is closely related to mathematical physics. The existing literature on the subject is vast and includes numerous books and journal papers.

A workshop was organized at the Erwin Schrödinger Institute for Mathematical Physics (Vienna) to give a snapshot of modern idempotent mathematics. This volume contains articles stemming from that event. Also included is an introductory paper by G. Litvinov and additional invited contributions.

The resulting volume presents a comprehensive overview of the state of the art. It is suitable for graduate students and researchers interested in idempotent mathematics and tropical mathematics.

Readership

Graduate students and research mathematicians interested in idempotent and tropical mathematics.

Table of Contents

• G. L. Litvinov -- The Maslov's dequantization, idempotent and tropical mathematics: A very brief introduction
• M. Akian, S. Gaubert, and V. Kolokoltsov -- Set coverings and invertibility of functional Galois connections
• M. Akian, S. Gaubert, and C. Walsh -- Discrete max-plus spectral theory
• A. Baklouti -- Dequantization of coadjoint orbits: Moment sets and characteristic varieties
• P. Butkovič -- On the combinatorial aspects of max-algebra
• G. Cohen, S. Gaubert, J.-P. Quadrat, and I. Singer -- Max-plus convex sets and functions
• A. Di Nola and B. Gerla -- Algebras of Lukasiewicz's logic and their semiring reducts
• W. H. Fleming and W. M. McEneaney -- Max-plus approaches to continuous space control and dynamic programming
• K. Khanin, D. Khmelev, and A. Sobolevskiĭ -- A blow-up phenomenon in the Hamilton-Jacobi equation in an unbounded domain
• G. L. Litvinov and G. B. Shpiz -- The dequantization transform and generalized Newton polytopes
• P. Loreti and M. Pedicini -- An object-oriented approach to idempotent analysis: Integral equations as optimal control problems
• P. Lotito, J.-P. Quadrat, and E. Mancinelli -- Traffic assignment & Gibbs-Maslov semirings
• D. McCaffrey -- Viscosity solutions on Lagrangian manifolds and connections with tunnelling operators
• E. Pap -- Applications of the generated pseudo-analysis to nonlinear partial differential equations
• E. Pap -- A generalization of the utility theory using a hybrid idempotent-probabilistic measure
• M. Passare and A. Tsikh -- Amoebas: Their spines and their contours
• J. Richter-Gebert, B. Sturmfels, and T. Theobald -- First steps in tropical geometry
• I. V. Roublev -- On minimax and idempotent generalized weak solutions to the Hamilton-Jacobi equation
• E. Wagneur -- Dequantisation: Semi-direct sums of idempotent semimodules
• J. van der Woude and G. J. Olsder -- On (min,max,+)-inequalities
• K. Zimmermann -- Solution of some max-separable optimization problems with inequality constraints